Title: Directional dependency of cepstrum on vocal tract length
Abstract: IN this paper, we prove that the direction of cepstrum vectors strongly depends on vocal tract length and that this dependency is represented as rotation in the n dimensional cepstrum space. In speech recognition studies, vocal tract length normalization (VTLN) techniques are widely used to cancel age- and gender-differences. In VTLN, a frequency warping is often carried out and it can be implemented as a linear transformation in a cepstrum space; c = Ac. However, the geometric properties of this transformation matrix A have not been well discussed. In this study, its properties are made clear using n dimensional geometry and it is shown that the matrix rotates any cepstrum vector similarly and apparently. Experimental results using resynthesized speech demonstrate that cepstrum vectors extracted from a speaker of 180 [cm] in height and those from another speaker of 120 [cm] in height are reasonably orthogonal. This result makes clear one of the reasons why children's speech is very difficult for conventional speech recognizers to deal with adequately.